Question

Qualitative analysis of an unknown acid found only carbon, hydrogen, and oxygen. In a quantitative analysis, a \(10.46 \mathrm{mg}\) sample was burned in oxygen and gave 22.17 \(\mathrm{mg} \mathrm{CO}_{2}\) and \(3.40 \mathrm{mg} \mathrm{H}_{2} \mathrm{O}\). The molecular mass was de- termined to be \(166 \mathrm{~g} \mathrm{~mol}^{-1}\). When a \(0.1680 \mathrm{~g}\) sample of the acid was titrated with \(0.1250 \mathrm{M} \mathrm{NaOH},\) the end point was reached after \(16.18 \mathrm{~mL}\) of the base had been added. (a) What is the molecular formula for the acid? (b) Is the acid mono-, \(\mathrm{di}\) -, or triprotic?

Short answer

The molecular formula for the acid is C4H6O4, and the acid is diprotic.

Step-by-step solution

Calculate the moles of CO2 and H2O formed

Using the given masses of CO2 and H2O, convert them to moles using their molar masses. The molar mass of CO2 is 44.01 g/mol and that of H2O is 18.02 g/mol. The number of moles of CO2 and H2O produced are calculated as follows:Moles of CO2 = mass of CO2 / molar mass of CO2Moles of H2O = mass of H2O / molar mass of H2O

Determine the moles of C and H in the sample

Each mole of CO2 contains one mole of carbon, so the moles of C in the original sample are equal to the moles of CO2. Similarly, each mole of H2O contains two moles of hydrogen, so to find the moles of H, multiply the moles of H2O by two.

Calculate the mass of O in the sample

To find the mass of oxygen, subtract the combined mass of C and H from the original sample mass. The mass of carbon is found by multiplying the moles of carbon by the molar mass of carbon (12.01 g/mol). The mass of hydrogen is obtained by multiplying the moles of hydrogen by the molar mass of hydrogen (1.008 g/mol).

Calculate the moles of O in the sample

Convert the mass of oxygen obtained in the previous step to moles of oxygen using the molar mass of oxygen, which is 16.00 g/mol. Moles of O = mass of O / molar mass of O.

Determine the empirical formula of the acid

To find the empirical formula, divide the moles of C, H, and O by the smallest number of moles present among them to get the simplest whole number ratio. This ratio provides the subscripts in the empirical formula.

Calculate the empirical formula mass

Add the masses of carbon, hydrogen, and oxygen in the empirical formula to find its molar mass.

Determine the molecular formula from the empirical formula

Divide the given molecular mass by the empirical formula mass. Multiply each subscript in the empirical formula by this number to find the molecular formula of the acid.

Calculate the moles of NaOH used in titration

Convert the volume of NaOH solution to moles using its concentration. Moles of NaOH = concentration of NaOH * volume of NaOH (in liters).

Determine the acid's proticity

Compare the moles of NaOH used in the titration with the moles of the acid. If one mole of NaOH reacts with one mole of the acid, it is monoprotic. If it takes two moles, it is diprotic, and if three moles, it is triprotic.

Key concepts

Empirical and Molecular Formula Determination

Understanding the difference between empirical and molecular formulas is a cornerstone of chemical quantitative analysis. An empirical formula represents the simplest whole number ratio of atoms in a compound, while the molecular formula shows the actual number of each type of atom in a molecule.

Let's go through an example. Imagine we have an unknown acid consisting of carbon (C), hydrogen (H), and oxygen (O). Through combustion analysis, we can determine the ratio of these atoms. For instance, if combustion of a sample produces carbon dioxide (CO₂) and water (H₂O), we can derive the amounts of carbon and hydrogen in the original sample. The remaining mass is assumed to be oxygen.

Determining Moles from Combustion Products

First, the mass of CO₂ and H₂O are converted to moles. Given the masses from combustion, the moles of carbon are equal to moles of CO₂, as each CO₂ molecule contains one carbon atom. Similarly, the moles of hydrogen are twice the moles of H₂O, because each water molecule has two hydrogen atoms.

Finding the Empirical Formula

The smallest number of moles for C, H, and O are used to calculate their mole ratio. This ratio is the empirical formula, which could be, for example, CH₂O. If we're given the molecular mass, as in the provided exercise, we can find the molecular formula by comparing the mass of the empirical formula with the actual molecular mass. If the molecular mass is a multiple of the empirical mass, you simply multiply the subscripts in the empirical formula by this factor to get the molecular formula.

Exercise Improvement Advice

To aid student comprehension, it's beneficial to include visual elements like diagrams to show the relationship between moles of combustion products and the moles of elements in the sample. Additionally, walking through a specific numerical example step-by-step can reinforce the concepts explained.

Stoichiometry of Combustion Analysis

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. In combustion analysis, stoichiometry is used to determine the amount of carbon, hydrogen, and sometimes other elements in an organic compound by burning the compound and analyzing the resulting carbon dioxide and water.

Applying Stoichiometry to Combustion

When a known mass of a compound is burned, stoichiometry allows us to deduce the moles of each element in the original compound based on the moles of the combustion products. For instance, a known mass of CO₂ will contain the same number of moles of carbon as was present in the original compound.

Calculating Elemental Moles

Stoichiometric coefficients relate the amount of product formed to the amount of reactant used. In the case of combustion, every one mole of CO₂ indicates one mole of carbon was present, and every one mole of H₂O indicates two moles of hydrogen were present, due to the stoichiometric coefficients in the balanced chemical equations for combustion.

Exercise Improvement Advice

Deepening understanding for students involves breaking down calculation steps and explaining the stoichiometric significance of each coefficient. For exercises involving combustion analysis, relating the process to real-world applications, like environmental monitoring or fuel efficiency calculations, can make the abstract concepts more tangible and easier to grasp.

Acid-Base Titration

An acid-base titration is a method used in chemistry to determine the concentration of a specific acid or base. This process involves adding a titrant of known concentration to a solution of the substance being tested until the chemical reaction is completed, as indicated by a color change (end point).

Titration Process and Calculation

A titration allows us to find out how much of an acid is present in a solution by reacting it with a known volume and concentration of a base (e.g., NaOH). The point at which neutralization occurs is used to calculate the amount of the substance of interest. The stoichiometry of the neutralization reaction provides a ratio that can be used to determine the amount of acid in the original solution.

For example, a known mass of acid is titrated with NaOH solution. Once the end point is reached, we use the volume and molarity (M) of the NaOH to find the moles of NaOH, which tells us the moles of the acid due to the stoichiometric relationship between the reactants in the neutralization reaction.

Identifying Acid's Proton Donating Ability

The moles of NaOH needed to reach the end point also reveal whether the acid is mono-, di-, or triprotic—meaning, it donates one, two, or three protons (H⁺) respectively, during the reaction. This knowledge is essential for understanding the acid's strength and reaction behavior.

Exercise Improvement Advice

Visually representing the titration setup and highlighting the color change at the end point can effectively illustrate the practical aspects of titrations. It can also be useful to emphasize the role of indicators in detecting the end point and to offer practice questions that challenge students to calculate the molarity of unknown solutions using titration data.